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What are they? How are they produced? How do x-rays interact with matter? How does the nature of the crystal effect that interaction?. X-Rays. Wilhelm R öntgen (1845-1923). Crook's Tubes. Crook's Tubes. Produced cathode rays Cathode rays were particles
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What are they? How are they produced? How do x-rays interact with matter? How does the nature of the crystal effect that interaction? X-Rays
Produced cathode rays Cathode rays were particles Cathode rays did not penetrate matter—they were not observed outside the tube. Cathode rays were charged. Crooks Tubes
The Discovery of X-rays in 1895 • Röntgen was working in a very dark lab with a Crook's tube. • Across the room was a watch glass containing Ba[Pt(CN)4] • Whenever the Crook's tube was turned on the watch glass glowed. • These were a new mysterious ray • Named x-rays
What are x-rays? • Are they waves or particles? • What is their wavelength (energy)? • How are they produced? • What more can be done with them? • A question that wasn't asked until much later is how safe are they?
X-rays are produced whenever an energetic electron beam interacts with matter. • The cathode rays were producing x-rays from the elements in the glass. • X-rays come off the target in all directions. • X-rays have wavelengths inversely proportional to the square root of the atomic number of the target material.
How does this happen? • The most intense line is the Kα line. • Do the incoming electrons knock out a 1S electron? Not likely. • Consider the electron cloud to be like the nucleus with many quantum states. • When an electron is added to the cloud, the cloud becomes unstable and emits radiation to return to the ground state.
Problems • Most of the electrons are simply conducted by the target. This produces a huge amount of heat in a small area. • For example, a power supply might provide 20ma at 50Kv or 1Kw of power. Of this ~97% will become heat. For a small beam a small target is required. Target melting. • Obviously it is important that there be a good vacuum between the filament and the anode or there will be arcing.
One Solution to the heat Problem • We can better dissipate the heat if we spin the target • This is a rotating anode generator • In this case the vacuum must be kept by pumps • Need a seal to hold 1x10-8mm vacuum and allow anode to spin at 3000-6000 rpm.
Rotating Anodes • Expensive to purchase • Expensive to maintain • ~12 fold increase in beam intensity • Various beam diameters are possible
Focusing Optics A multilayer optic is produced by depositing alternating layers of light-element- and heavy-element-containing materials onto a substrate. The layer thickness acts like the d spacing in a crystal in the sense that X-rays impinging on a multilayer optic at the proper θ angle will produce a monochromatic diffracted X-ray beam. If the layer thickness is varied across a pre-curved substrate, a graded optic can be produced that captures a larger angle of X-rays from the source and produces either a focused or parallel X-ray beam.
Rigaku MM002+ • Uses a Copper target. • The electron beam is focused using magnets to produce a small size. • The x-rays go through an optics system • Current 0.88ma Voltage 45Kv vs for a regular tube 20ma and 50Kv. • Intensity is roughly 5 times greater than tube. • Spot size 0.1 mm vs 0.4 mm • The unit uses 110v and plugs into a standard outlet.
Need Even More Intensity • Want 2 to 3 orders of magnitude or more. • Want tunable wavelength • Want very small beam size • Use a synchrotron. • Accelerate electrons to near the speed of light and have them circle around a large circle • Only standing waves of the circle diameter will be allowed
Which Wavelength to Use • Generally use Cu 1.5418Å or Mo 0.71073Å • The longer the wavelength the farther apart the diffraction spots are in space. For large unit cells like macromolecules use Cu. As the distance between spots is reciprocal to the cell dimensions. • Cu produces more x-rays and the detectors have a higher efficiency in measuring them. • Mo is not as absorbed as Cu. Best for heavy element problems. • Move back to copper lately.
Medical Xrays vs Crystallography • Medicine needs penetrating x-rays—so short wavelength. • The power loading on the target is limited by its melting point—want high melting metal • Medical x-rays use a tungsten target—0.15Å • Since the x-rays are on for less than a second do not need to worry about variations in the beam.
Desired Properties of the Beam • Monochromatic • Parallel • Coherent • In phase
Monochromation • Simplest is β filter • Crystal monochromator • Can use a crystal to monochromate by collecting some Bragg spot • Typically today use graphite (2-dimensional crystal) • All methods involve considerable loss of intensity
Making the Beam Parallel • Done using a collimator • This is a long, narrow tube which eliminates all x-rays that are not travelling down the tube. • More loss of intensity • This results in a beam which has a region of uniform intensity the size of the collimator opening. However, there are x-rays that are outside this sweet spot with lesser intensity • For light this could be done using lens.
Coherence • This means all the waves are in phase. • This cannot be achieved for electron beam produced x-rays. • Therefore, there will be some interference between waves. • Synchrotron is coherent, parallel and exactly monochromatic!
Polarization • X-ray source is not polarized • For light a laser would have all the correct properties. • No x-ray lasers. • The energy need to achieve lasing is inversely related to the square of the frequency of radiation to be produced. • Comparing green light (1/5000) vs x-ray (1/1) it is 2.5x107 times more difficult.
Safety • Beam is very small • Hard to get body parts in the beam • Radiation is lower energy. • Many interlocks to prevent accidental exposure • Ba impregnated plexi-glass blocks radiation • Still—be sure you know what you are doing!!
Simplest Interaction of Radiation with Matter (one photon). • Transmission—the radiation passes through the material. • Absorption—the radiation is absorbed by the material. The energy must be dissipated! • These processes are inverse –that is probability(absorption)=1.-probability(trans) • Neither play any role in crystallography beyond the fact that absorption is a nuisance that must be corrected.
More complicated Interactions • In the 1890's J. J. Thompson worked out the scattering of a electromagnetic radiation by a free electron. • It is this process that is the source of the photons in the x-ray diffraction experiment. • Note that scattered photons come off in all directions and have a phase 180° to the incident wave. • Assume elastic scattering—no change in energy
The amplitude of the scattered wave is about 2.82x10-13 times less than the incoming wave at any point. This is for elastic scattering where the frequency of the scattered wave is the same as the incoming wave This is the scattering at a point for 1 electron. There actually also needs a distance term r (the units are cm) but we will assume we are 1 cm from the scattered electron. J.J. Thompson Scattering
More on Scattering Scattering where the plane of the scattered wave is the same as the incident radiation has the same probability regardless of the direction • Scattering out of the plane falls off by cos2(2θ) Since any wave can be broken down into two components (in the plane and out of the plane) the fall off for an unpolarized beam is (1+cos2(2θ))/2. This is the polarization factor.
The Take Home Message • The electrons scatter the x-ray radiation. Each atom scatters proportional to its atomic number • The scattered waves interfere with each other because of the periodic nature of the crystal. • The distance between the spots is inversely related to the repeat distance. • The pattern of the individual scatterers is contained in the intensity of each spot. • By applying a Fourier series the intensity can be converted to the scattering arrangement.
